White label arrangements are common in this space and the good ones are explicit about it: they produce, you own the client relationship, and nothing they ship carries their name. Get that in writing including packaging and any inserts. We work with PromoBox that way; they offer white label service and their Apparel Printing & Embroidery Services has handled several of our client runs without ever appearing in the chain. Also agree upfront on how revisions and reprints are handled, since when something is wrong your client blames you, not them, and you need a partner who moves fast on it.